Question

tranpo oprtn/logistics mgmt

Problem #1(15 marks) Mai Lao Industries manufacture 70 tonnes of goods a week in factory A and 50 tonnes a week in factory B. The map co-ordinates of these factories are (14,11) and (54,48) respectively. These goods are delivered to 14 main customers whose average weekly requirements and co-ordinates are shown below. The company wants to improve its customer service and decides to open a logistics centre. There are four possible locations, each with the same operating costs, located at (20,8), (61,19), (29,32) and (50,22). Which of these locations is best? Customer Demand Co-ordinates Customer Demand Co-ordinates 1 (12,69) 4 (11,16) 8 16 2 1 (30,9) 2 (27,38) 3 8 (43,27) 10 4 (51,6) 7 (54,52) 11 6 (43,16) 5 17 (29,62) 12 3 (54,16) 6 10 (11,51) 13 12 (12,60) 7 15 (8,10) 14 18 (12, 3) Also find the center of gravity of the above data.

Answer 1

Ans: The best alternative way will be chosen based on the shortest way with less traffic and more comfort. (29,32) will be the best possible alternative because while taking the average distances of x & y coordinates the mean distance will be around (28,31). As far as consider this will be serves as the middle point of the both supplier location and factory location. The factory A will be very close to the Logistics area where as Factory B somewhat distant from the Logistics area. So , to avoid inconvenience the farthest area from the middle point can be served by Factory B. Besides this this location serves as the middle where as remaining three will be the corners of the sides.

yi yiAi xi xiAi Area X Centre of gravity of X 11 16 176 5.5 8 968 1408 A1x1+A2x2+A3x3+.... 30 9 270 15 4.5 4050 1215 A1+A2+A3+... 43 27 1161 21.5 13.5 24961.5 15673.5 75816 54 52 2808 27 26 73008 Centre of gravity of Y 26071 Alyl+A2y2+A3y3+... 29 62 1798 14.5 31 55738 11 51 561 5.5 25.5 3085.5 14305.5 A1+A2+A3+... 8 10 80 4 320 400 12 69 828 34.5 4968 28566 27 38 1026 13.5 19 13851 19494 51 6 306 25.5 3 7803 918 43 16 688 21,5 14792 5504 23328 54 16 864 27 6912 12 60 720 6 30 4320 21600 12 3 36 6 1.5 216 54 204550 11322 244796 Centre of Gravity X 18.0666 Centre of Gravity Y 21.6213 T